Casimir-Polder interaction between an atom and a dielectric grating

TL;DR

This paper introduces a scattering approach to precisely compute the Casimir-Polder potential between a ground-state atom and a dielectric grating, enabling analysis for various geometries and comparing results with approximations.

Contribution

The authors develop an exact formalism for calculating dispersive Casimir-Polder interactions with arbitrary grating parameters, advancing beyond previous approximate methods.

Findings

Potential is nearly sinusoidal at moderate distances

Exact calculations match proximity force approximation at larger distances

Method applicable to arbitrary grating geometries

Abstract

We develop the scattering approach to calculate the exact dispersive Casimir-Polder potential between a ground-state atom and a rectangular grating. Our formalism allows, in principle, for arbitrary values of the grating amplitude and period, and of the atom-grating distance. We compute numerically the potential for a Rb atom on top of a Si grating and compare the results with the potential for a flat surface taken at the local atom-surface distance (proximity force approximation). Except for very short separation distances, the potential is nearly sinusoidal along the direction transverse to the grooves.